A343321 - OEIS

%I #34 Jun 06 2021 15:50:11

%S 0,0,0,0,0,1,1,2,3,4,1,4,3,5,5,4,4,6,5,7,2,6,5,8,5,4,6,7,6,8,2,8,6,7,

%T 7,5,5,8,7,8,2,8,6,9,6,3,7,9,5,8,3,8,6,8,6,5,6,7,7,9,1,8,7,8,6,4,6,9,

%U 6,7,3,9,5,8,7,4,6,8,6,9,2,7,7,9,5,4,7

%N Number of knapsack partitions of n with largest part 5.

%C An integer partition is knapsack if every distinct submultiset has a different sum.

%C I computed terms a(n) for n = 0..10000 and (6,7,7,5,5,8,7,8,2,8,6,9,6,3,7,9,5,8,3,8,6,8,6,5,6,7,7,9,1,8,7,8,6,4,6,9,6,7,3,9,5,8,7,4,6,8,6,9,2,7,7,9,5,4,7,8,6,8,2,9) is repeated continuously starting at a(32).

%H Fausto A. C. Cariboni, <a href="/A343321/b343321.txt">Table of n, a(n) for n = 0..1000</a>

%e The initial values count the following partitions:

%e    5: (5)

%e    6: (5,1)

%e    7: (5,1,1)

%e    7: (5,2)

%e    8: (5,1,1,1)

%e    8: (5,2,1)

%e    8: (5,3)

%Y Cf. A108917, A275972, A326017, A326034, A344310.

%K nonn

%O 0,8

%A _Fausto A. C. Cariboni_, May 14 2021